Generalizations
Witt groups can also be defined in the same way for skew-symmetric forms, and for quadratic forms, and more generally ε-quadratic forms, over any *-ring R.
The resulting groups (and generalizations thereof) are known as the even-dimensional symmetric L-groups L2k(R) and even-dimensional quadratic L-groups L2k(R). The quadratic L-groups are 4-periodic, with L0(R) being the Witt group of (1)-quadratic forms (symmetric), and L2(R) being the Witt group of (-1)-quadratic forms (skew-symmetric); symmetric L-groups are not 4-periodic for all rings, hence they provide a less exact generalization.
L-groups are central objects in surgery theory, forming one of the three terms of the surgery exact sequence.
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